Continuous steepest descent in Hilbert space: Linear case

1997 ◽  
pp. 11-13
Author(s):  
John William Neuberger
Keyword(s):  
Hilbert Space ◽  
Steepest Descent ◽  
Linear Case

scholarly journals The behavior of solutions of non-linear differential equations in Hilbert space. I

1988 ◽  
Vol 11 (1) ◽  
pp. 143-165 ◽  
Author(s):  
Vladimir Schuchman
Keyword(s):  
Hilbert Space ◽  
Cauchy Problem ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Linear Differential Equations ◽  
Linear Case ◽  
Cauchy Problems ◽  
The Cauchy Problem ◽  
Linear Differential ◽  
Degenerate Linear

This paper deals with the behavior of solutions of ordinary differential equations in a Hilbert Space. Under certain conditions, we obtain lower estimates or upper estimates (or both) for the norm of solutions of two kinds of equations. We also obtain results about the uniqueness and the quasi-uniqueness of the Cauchy problems of these equations. A method similar to that of Agmon-Nirenberg is used to study the uniqueness of the Cauchy problem for the non-degenerate linear case.

Steepest descent in the Hilbert space - A method for calculating state vectors of ground and excited states

1986 ◽  
Vol 116 (9) ◽  
pp. 403-406 ◽  
Author(s):  
J. Ftáčnik ◽  
J. Pišút ◽  
V. Černý ◽  
P. Prešnajder
Keyword(s):  
Hilbert Space ◽  
Excited States ◽  
Steepest Descent

Steepest Descent and Least Squares Solvability

1974 ◽  
Vol 17 (2) ◽  
pp. 275-276 ◽  
Author(s):  
C. W. Groetsch
Keyword(s):  
Hilbert Space ◽  
Linear Operator ◽  
Least Squares ◽  
Bounded Linear Operator ◽  
Steepest Descent ◽  
Normal Equation ◽  
Bounded Linear ◽  
Least Squares Solution ◽  
Image Position

Let T be a bounded linear operator defined on a Hilbert space H. An element z∈H is called a least squares solution of the equationif . It is easily shown that z is a least squares solution of (1) if and only if z satisfies the normal equation

An Introduction to Hilbert Space

1988 ◽  
Author(s):  
N. Young
Keyword(s):  
Hilbert Space
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